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Active Learning for Fair and Stable Online Allocations

Riddhiman Bhattacharya, Thanh Nguyen, Will Wei Sun, Mohit Tawarmalani

TL;DR

The approach hinges on an active-learning procedure that carefully selects the agent from whom to gather feedback, ensuring its effectiveness in the allocation process, and introduces a deliberate constraint on feedback, restricting it to a single agent or a limited number of agents per period.

Abstract

We explore an active learning approach for dynamic fair resource allocation problems. Unlike previous work that assumes full feedback from all agents on their allocations, we consider feedback from a select subset of agents at each epoch of the online resource allocation process. Despite this restriction, our proposed algorithms provide regret bounds that are sub-linear in number of time-periods for various measures that include fairness metrics commonly used in resource allocation problems and stability considerations in matching mechanisms. The key insight of our algorithms lies in adaptively identifying the most informative feedback using dueling upper and lower confidence bounds. With this strategy, we show that efficient decision-making does not require extensive feedback and produces efficient outcomes for a variety of problem classes.

Active Learning for Fair and Stable Online Allocations

TL;DR

The approach hinges on an active-learning procedure that carefully selects the agent from whom to gather feedback, ensuring its effectiveness in the allocation process, and introduces a deliberate constraint on feedback, restricting it to a single agent or a limited number of agents per period.

Abstract

We explore an active learning approach for dynamic fair resource allocation problems. Unlike previous work that assumes full feedback from all agents on their allocations, we consider feedback from a select subset of agents at each epoch of the online resource allocation process. Despite this restriction, our proposed algorithms provide regret bounds that are sub-linear in number of time-periods for various measures that include fairness metrics commonly used in resource allocation problems and stability considerations in matching mechanisms. The key insight of our algorithms lies in adaptively identifying the most informative feedback using dueling upper and lower confidence bounds. With this strategy, we show that efficient decision-making does not require extensive feedback and produces efficient outcomes for a variety of problem classes.
Paper Structure (21 sections, 237 equations, 6 figures, 4 algorithms)

This paper contains 21 sections, 237 equations, 6 figures, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Max-min Fairness for Unit Demand Agents
  4. A Special Example: Top $K$-Arm Identification
  5. Our Algorithm and Regret Analysis
  6. Allocation of Bundles
  7. Max-Min Fairness
  8. Our Algorithm and Regret Analysis
  9. Minimal Envy Fairness
  10. Stable Assignment
  11. Model
  12. Learning Task and Regret Measures
  13. Algorithm
  14. Simulations
  15. Conclusion
  16. ...and 6 more sections

Figures (6)

  • Figure 1: Outline of the four interconnected problems addressed in our paper.
  • Figure 2: Illustration of an allocation with bundle $\phi(j)$ being allocated to agent $j$.
  • Figure 3: Comparison between the proposed Dueling ULCB and the two benchmark methods.
  • Figure 4: Cumulative regrets of our Dueling ULCB algorithm with varying $K$ and varying $N$.
  • Figure 5: Cumulative regrets of the Dueling Max-Min ULCB algorithm with varying reward functions for both agents.
  • ...and 1 more figures